# State the domain and range of each relation {(-2, 3.5), (0, 5.25), (-2, -8.75)}. Then determine whether or not each relation is a function, and justify your answer?

Jan 1, 2018

The domain is the set: $\left\{- 2 , 0\right\}$.
The range is the set: $\left\{- 8.75 , 3.5 , 5.25\right\}$.
This relation does not represent a function.

#### Explanation:

When presented this way, the domain element is the first value in the ordered pair and the range element is the second value in the ordered pair. So it looks like: (domain, range).

We have:
$\left\{\begin{matrix}- 2 & 3.5 \\ 0 & 5.25 \\ - 2 & - 8.75\end{matrix}\right\}$

So just listing elements we have:
domain elements are $- 2$, $0$, and $- 2$.
range elements are $3.5 , 5.25 ,$ and $- 8.75$.

Since $x = - 2$ is associated with two $y$-values, we know this relation does not represent a function. (The definition of a function is that each element of the domain is associated with only one element of the range.)

So the domain is the set: $\left\{- 2 , 0\right\}$.
The range is the set: $\left\{- 8.75 , 3.5 , 5.25\right\}$.